Invited Session Fri.3.H 3021

Friday, 15:15 - 16:45 h, Room: H 3021

Cluster 7: Finance & economics [...]

Optimization in financial markets


Chair: Teemu Pennanen



Friday, 15:15 - 15:40 h, Room: H 3021, Talk 1

John Schoenmakers
Multilevel primal and dual approaches for pricing American options

Coauthors: Denis Belomestny, Marcel Ladkau


In this talk we propose two novel simulation based approaches for
for pricing American options. (I) The first one is in fact a multi level version of the nested Monte
Carlo dual algorithm of Andersen and Broadie (2004),
whereas the second one (II) is a multi level version of simulation based
policy iteration (cf. Kolodko Sch. 2006), hence a primal approach.
The multilevel concept is applied to the number of sub-simulations needed for constructing
a dual martingale in (I) and for iterating to a new policy in (II). In both cases the overall complexity turns out to be
significantly reduced.
%(I) is joint work with Denis Belomestny, (II) is joint work with Denis Belomestny and Marcel Ladkau.



Friday, 15:45 - 16:10 h, Room: H 3021, Talk 2

Ari-Pekka Perkkiƶ
Stochastic programs without duality gaps

Coauthor: Teemu Pennanen


This talk is on dynamic stochastic optimization problems parameterized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.



Friday, 16:15 - 16:40 h, Room: H 3021, Talk 3

Dirk Becherer
Optimal sparse portfolios in continuous time


We discuss sparse portfolio optimization in continuous time.
Optimization objective is to maximize the classical expected utility, that
is the expectation of a concave functional of portfolio gains.
Sparse optimization aims to find asset allocations that contain only few
assets or that deviate only in few coordinated from a reference benchmark
allocation. Results show that optimal sparse portfolios are less
sensitive to estimation errors and performance is superior to optimal
portfolio without sparsity constraints, when estimation of model parameters
is taken into account.


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